The Steam version of the game has 83 achievements, some of which are quite hard to reach.
Self explanatory Edit
Animal whisperer - Tame an animal [Easy way is to be a bard, than meet an animal and play "u"se instrument].
Assassin's deed - Kill an enemy with poison. [Assassins start with poison potions, so player can coat character's weapon by dipping it into potion of poison, after that any injured monster is poisoned, so you need to hit and wait for it/him to drop dead].
Atonement - Recover from being doomed.
Aware of danger - pass the Small cave in less than 200 turns. ('Pass' means hitting downstairs to UD1).
A child's hero - Save a puppy from certain doom. (Whether wished for puppies count needs confirmation.)
Battle alchemist - Kill monster with alchemical fireball. (Well, only for chracters with alchemy skill. You need to mix any two potions who are not recipe and have monster close, fire resistance recommended).
Bookworm - Get the Weird tome.
Champion of Balance - Be crowned as a champion of Balance (neutral crowning).
Champion of Chaos - Be crowned as a champion of Chaos (chaotic crowning).
Champion of Order - Be crowned as a champion of Order (lawful crowning).
Deep dive - reach lv50 of infinite dungeon.
Dragon slayer - Slay a dragon. Easy, right?
Egyptologist - Kill the lord of the mummies.
Entomologist - Enter the bug infested temple. (This unlocks upon entering the second level of that place, needs 100 character deaths in the logfile.)
Filk will never die! - Kill Filk. [Killing Filk is obligatory for any ultra ending anyway]
Fortune's Favor - Have Fate smile upon you. [Whether gaining this intrinsic through equipment is enough needs confirmation].
It starts easy - Die your first death.
Just in time - Save Khelavaster.
Lucky sip - Get a wish from a pool.
Mad carpenter no more - Find a way to cure Yrrigs.
Martial arts adept - Gain level 5 in unarmed fighting.
Master alchemist - Mix a potion of gain atributes. (In order to know recipe, character needs Alchemy at 100)
Master of Air - Obtain the Air Orb.
Master of Earth - Obtain the Earth Orb.
Master of Fire - Obtain the Fire Orb.
Master of Mana - Obtain the Mana Orb.
Master of Water - Obtain the Water Orb.
Peaceful - Offer peace to a monster.
Power at my fingertips - successfully learn the 'Wish' spell from a tome. (You need to read spellbook of wish, wizards get one guaranteed in the library).
Sacrificial fodder - Dealt successfully with the demented ratling.
Scorer - Score 10 million points.
High scorer - Score 25 million points.
Scoring monster - Score 50 million points [Currently fast paced Ultimate chaos ending seems to give the best score].
Shoplifter - Successfully rob a shop without resorting to violence. [ The easiest way is to teleport out of the shop].
Theseus - Get the minotaur axe.
Things were better back then. - Restore a character form permadeath. (Essentialy you need to get AoLS, wear it and die to cheat the death and unlock the achievement. Although necromancer's class power should work too.).
There is nos such thing as overkill - Obtain the Trident of the Red Rooster.
Very deep dive - Reach level 100 of the infinite dungeon.
Visited Terinyo - Locate and enter the town of Terinyo.
What's this? - Find a strange item.
Why did you do that? - Finish Riurry's quest?
Well-known Wanderer - Rise to experience level 5.
Well-known Veteran - Rise to experience level 10.
Well-known Champion - Rise to experience level 20.
Well-known Hero - Rise to experience level 30.
Well-known Demi-Urge - Rise to experience level 50.
Achiever - Unlock 40% of all achievements.
Overachiever - Unlock 80% of all achievements.
Adom grandmaster - Unlock every other achievement.
Requires to win the game Edit
...And throw away the key - Close the chaos gate.
Beloved by fate - win the game with a character by letting fate decide.
Consistent believer - Win without ever changing alignment. [Changes within neutral, lawful or chaotic alignment do not have influence on this -- for example change from L+ to LN is okay].
Everything for this moment - Usurp the throne of Chaos (Chaos god ending).
Magic hater - Win without casting spells.
Plant hater - Win without using herbs, plants or any related skills. [herbs, logs, Gardening, Woodcrafting, maybe various types of bread too, aplles and melons were reported not to disable this achievement].
Plutonium man - Complete the game after killing 95% of every type of non-unique monster in the game. (This one is currently bugged and unlocks at lower percentage).
Speed Demon - Complete the game within 10000 turns. (Best melee speed runs are >18.000 turns, so being a caster is the way to go).
Speed Runner - Complete the game within 20000 turns.
Speed Player - Complete the game within 40000 turns.
The Grey Hawk - Become Avatar of Balance (neutral ultra ending)
The White Eagle - Become Avatar of Order (lawful ultra ending).
Titanium man - Complete the game before rising above experience level 20. (Hitting lv20 apparently is not allowed, heavy use of pets is recommended, since chracter must win at lv19 max.)
Yep, all done! - Leave the Drakalor Chain after having closed the chaos gate.
Tricky ones Edit
Avatar of thieves - Steal an item worth at least 6666 gold. [6666 must be base item cost, not a shop price. The only confirmed item which works is an amulet of resurrection, although some other artifacts should be enough].
Give and take - Buy stuff with a total value of 90, 169 gold pieces with one character. (90169 is the sum collected by the resurrection campaign. For achievemnt game counts buys only, thus character can sell and buy same stuff repeatedly. The best way to achive the exact sum is selling rocks.)
Globetrotter - Visit every town in Ancardia. [Dwarftown, Terinyo, bandit village, HMW, ruined city (Reportedly this one triggers in a buggy way, exact reasons are not known, but main suspects are Dwarftown at certain depth. Eitehr player needs to see all possible incranations of Dwarftown or just one on particular depth].
Iron man - Rertieve Chaos Sceptre in the most straightforward way possible, then leave the game. (You can't enter any otehr locations ecept wilderness and Infinite dungeon. So it is best to head straight to Infinite dungeon and get the sceptre. Going up stairs or away from downstairs is allowed under achievements rules.)
Ocean's Eleven - Successfully rob the Casino. (If you end attacking shopkeeper before stealing, it will not count since it's 'mugging'. The easiest way is to block doorway with pet and swap with him later on.)
Eternium man - Level up to level 50 in Small cave without visiting any other location. [Since widlerness is alowed it is possible to do Steelman stop close to lv50 and finish leveling in small cave. Doing so, however, breaks spirit of classical Adom challenge. Proper way to do it so far unknown].
Lithium man - Complete the game without visiting any locations except the Caverns of Chaos and the Tower of Eternal Flames (Currently this one is bugged, one needs to avoid Animated Forest, Ogre cave and other optinal CoC branches (like blue dragon caves)).
Steel man - Level up to level 50 in the wilderness without entering any location. (Typically player raises wilderness DL by reading scroll of dangers, scums for RoDS and wishes for 'Emperor Moloch', killing resulting horde of greater molochs gives enough experience to reach lv50).